1. In the courtroom. These people could have received a faster, more painless, and more just trial. The proceedings could have been more open, easier to search and data mine, and hence easier to react to faster. Additionally (and somewhat science-fictiony) I personally would like to see us experiment with alternative juries - particularly much larger, distributed juries. If justice can't be crowd-sourced, then I don't know what can.

2. In the legislature. Although the creation of bills is an intensely collaborative process, too often the details are delegated to underlings, and those details are seriously misinformed by the facts. So one piece of software that is needed world wide are better document collaboration tools that are tied to accurate sources. The legislature in particular should be obsessively concerned about how the justice system is applying their laws. Better visibility into what's happening, in real-time, would make the legislature a) more aware and b) more responsive to injustice.